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Energy stored in capacitors is represented by $$U = \frac{1}{2} QV$$

Now I have heard 2 reasons why there’s a half factor, unlike the general potential energy equation, which is $U = QV$.

  1. Capacitors should’ve stored $QV$ amounts of energy. But, because electrons are being pushed to a negative plate, and electrons are being pulled off from an increasing positive plate, work is being done and half of $QV$ is needed to do work. The remaining half is the energy stored in capacitors.
  2. When you are discharging a capacitor, voltage keeps on decreasing as charge keeps on decreasing. As a result, energy keeps on decreasing and the sum of the energy transferred happens to be half of $QV$.

I don’t really know what’s the correct way to approach this. Both sound equally valid to me.

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Reason 1: It takes work to keep pushing electrons onto the capacitor plate, to overcome the electric repulsion. Half the energy is lost to this.

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